Question

Find the ratio of the AM and CD sections when :(a) AM = 18 cm, CD = 48 cm;(b) AM = 1m 2 cm, CD = 36 dm.

Answer 1

To find the ratio between 2 quantities, they must have the same unit of measurement

(a)

Since AM = 18 cm

Since CD = 48 cm

Then we can find the ratio between them directly because they have the same unit

`AM:CD=18:48`

We need to simplify the ratio

Since the greatest common factor of 18 and 48 is 6, then

Divide the terms of the ratio by 6 to simplify it

`\begin{gathered} AM:CD=(18)/(6):(48)/(6) \\ AM:CD=3:8 \end{gathered}`

The ratio between AM and CD is 3: 8

(b)

Since AM = 1 m 2 cm

Since CD = 36 dm

Then we can not find the ratio directly because they have different units of measurement, then we will change both to cm

Since 1 m = 100 cm, then

AM = 1 x 100 + 2 = 102 cm

Since 1 dm = 10 cm, then

CD = 36 x 10 = 360 cm

Now, we can find the ratio between then

`AM:CD=102:360`

Since the greatest common factor of 102 and 360 is 6, then divide each term by 6 to simplify the ratio

`\begin{gathered} AM:CD=(102)/(6):(360)/(6) \\ AM:CD=17:60 \end{gathered}`

The ratio between AM and CD is 17: 60